Research Areas
Algebra
Research developed within the Algebra group connects with a variety of (sub)areas of Mathematics and Computer Science. Graph-theoretic, geometric or topological arguments have widespread use. The research of the Algebra group covers areas such as Automata theory, Combinatorics, Dynamical systems, Group theory, Representation and ring theory, Semigroup theory.
Analysis
The Analysis group conducts research in a wide variety of topics, including integral equations and operator theory, special functions and orthogonal or multiple orthogonal polynomials for the analysis and solution of differential problems. The research covers a wealth of different perspectives on mathematical analysis from theoretical aspects, numerical analysis, scientific computing and applications.
Computational Mathematics
Computers have fundamentally changed the relationship between mathematics, computing and other sciences. Apart from their invaluable role in numerical, symbolic and experimental applications, computation is per se an important object of mathematical study, constantly proposing new challenges for mathematics. The research line Computational Mathematics has developed from the recognition by CMUP members of the intense and important computational effort that was being undertaken independently in different areas of Mathematics.
Dynamical Systems
The theory of Dynamical Systems has its origin in the qualitative study of ordinary differential equations or difference equations. Our research addresses these types of systems, with time varying in a continuous, discrete or complex way. We study algebraic, analytic, geometric, probabilistic and topological properties of systems, with some problems arising in Biology, Economics, and Engineering.
Geometry
Geometry is a central area of modern mathematics. The 3 main strands of our work (described by the keywords) are closely intertwined, through the use of dynamical (symplectic) methods in the study of geometric problems, on the one hand, and the use of geometric methods in the study of problems in dynamics, on the other. We also contribute with applications to Economics and Biology, in the line Mathematical Models and Applications.
Mathematical Models and Applications
Many of CMUP's researchers work on applications of Mathematics to other subjects in science and technology. For some, this is the main aspect of their research; for others, applications appear as interesting uses for their mathematical expertise. Some involve direct analysis of real world data and case studies, done in close connection with research groups outside CMUP that specialise in the area of application, including international reference research groups. In other cases, the project consists on either the analysis of existing mathematical models or in the development of new models.
Probability and Statistics
The group of Probability and Statistics aggregates researchers from CMUP with the common denominator that they all use tools of probability and statistics to carry out research. The research subjects covered include ergodic theory, extreme value theory, signal processing and statistical modelling and inference. Moreover, applications to biomedicine, engineering, insurance and meteorology are also studied.
Semigroups, Automata and Languages
Research in this area ranges from algebraic topics such as semigroups and groups (finite, profinite, or general) to mathematical models used in computer science, namely various flavors of automata and formal languages. Current work aims not only to contribute to the theories of each of the topics but also to explore the connections between them, with applications in both directions.
